Noise reduction blur / postprocess in blender
Blender Compositor work only in 2D too..

"using some extended info that Blender has?" - You show a Photo.. What Info should Blender have that PS doesn't? ;-)

What you have in your Image here is actually not Noise, but Compression Artefacts.  

I found this solution with Bilateral Blur works quite ok on your Sample:



I doubt that any Noise Reduction on Images(not rendered) in Blender is much better than dedicated ones in Gimp or elsewhere. While Blenders Compositor allows some neat things, it does not give direct access to Pixels, which i think is needed for any decent Noise reduction. (Of course Node do access Pixels, but you have no way of access Pixels in you Node Setup)